2.07 PRE-CALCULUS

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Teacher: Jerry Arnold
Textbook: Precalculus: Mathematics for Calculus, 2012
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Obj #
 Unit
 Objective:
"The learner will . . ."
 Standard(s)
 No. of Days
 Vocabulary Terms
 Resources
 Student Learning Activities
 Assessment
1
 1
 understand and apply the properties of real numbers
 12.1.1[b] 12.1.2[a,b]
12.1.3[a] 12.3.3[g,h]
integer, rational, irrational, intersection, union
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
2
 1
 define and apply integral exponents and rational exponents
 12.1.1[a,b]
12.1.3[a,b,c] 12.3.3[b]
growth and decay, laws of exponents
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
3
 1
 manipulate and solve basic algebraic equations
 12.3.3[c,d,e,i,l]
variable, monomial, binomial, polynomial
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
4
 1
 simplify, perform algebraic operations on and solve rational expressions
 12.3.1[b] 12.3.3[j,k,o]
domain, compound fraction
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
5
 1
 find the intersection of two lines and find the length and midpoint of a segment
 12.1.4[a,b]
12.2.2[a,b,c] 12.2.4[a]
12.3.1[c,e]
 1
 coordinates, x-axis, y-axis, origin, quadrants, x-coordinate, y-coordinate, graph, x-intercept, y-intercept, linear equation, general form, solution
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
6
 1
 find the slope of a line and determine whether two lines are parallel, perpendicular, or neither
 12.2.2[a] 12.3.1[c,d,e]
 1
 slope, parallel, perpendicular, rise, run, slope-intercept form, negative reciprocal
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
7
 1
 find an equation of a line given certain geometric properties of the line
 12.2.2[a] 12.3.1[c,d,e]
12.3.3[f,g]
 1
 point-slope form, intercept form,
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
8
 1
 model real-world situations by means of linear functions
 12.1.4[a,b]

12.2.4.ab
12.3.1.abcdef
 1
 function, domain, range, zero
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
9
 1
 solve quadratic equations using different methods
 12.3.1[e] 12.3.3[e,f,g,h,i]
quadratic equation, discriminant, quadratic formula, completing the square, root
 textbook, chapter 1
 practice exercises, notes
 HW, quizzes, test
10
 2
 identify a function, determine the domain, range, and zeros of a function, graph a function
 12.3.1[a,b,c,d,e,h,i]
dependent variable, independent variable, domain, range, vertical line test
 textbook, chapter 2
 practice exercises, notes
 HW, quizzes, test
11
 2
 perform operations on functions and determine domains of resulting functions
 12.3.3[c,d,n]
sum, difference, product, quotient, composition
 textbook, chapter 2
 practice exercises, notes
 HW, quizzes, test
12
 2
 reflect graphs and use symmetry to sketch graphs
 12.2.3[a,b]
reflection, line of symmetry, point of symmetry
 textbook, chapter 2
 practice exercises, notes
 HW, quizzes, test
13
 2
 determine periodicity and amplitude from graphs, stretch and shrink graphs both vertically and horizontally, translate graphs
 12.2.3[a,b]
periodic, fundamental period, amplitude, stretching, shrinking, translating
 textbook, chapter 2
 practice exercises, notes
 HW, quizzes, test
14
 2
 find the inverse of a function, if the inverse exists
 12.3.1[e,h]
inverse, horizontal line test, one-to-one function
 textbook, chapter 2
 practice exercises, notes
 HW, quizzes, test
15
 3
 define and graph quadratic functions
 12.3.1[a,b,d,e] 12.3.2[a,c,d] 12.3.3[i]
quadratic function, vertex, axis of symmetry, parabola
 textbook, chapter 3.1
 practice exercises, notes
 HW, quizzes, test
16
 3
 model real-world situations using quadratic functions
 12.2.4[b] 12.3.1[a,e] 12.3.2[a,d]
curve-fitting, quadratic model
 textbook, chapter 3.1
 practice exercises, notes
 HW, quizzes, test
17
 3
 graph a polynomial function and determine end behavior and zeros
 12.3.1[a,d,e,i]
12.3.2[d] 12.3.3[e,l]
polynomial, terms, coefficients, leading term, degree, maxima, minima, leading term
 textbook, chapter 3.2
 practice exercises, notes
 HW, quizzes, test
18
 3
 use long and synthetic division and apply the remainder and factor theorems
 12.3.3[b,c,d,e]
synthetic division, factor theorem, remainder theorem
 textbook, chapter 3.3
 practice exercises, notes
 HW, quizzes, test
19
 3
 solve polynomial equations by various methods of factoring, including the use of the rational root theorem
 12.3.1[d] 12.3.3[d,e,i]
rational root theorem
 textbook, chapter 3.4
 practice exercises, notes
 HW, quizzes, test
20
 3
 add, subtract, multiply and divide complex numbers
 12.1.1[a,b] 12.1.3[a]
12.3.3[d,e]
complex number, imaginary number, pure imaginary, complex conjugates
 textbook, chapter 3.5
 practice exercises, notes
 HW, quizzes, test
21
 3
 apply general theorems about polynomial equations
 12.1.3[a] 12.3.3[d,e]
fundamental theorem of algebra, complex conjugates theorem
 textbook, chapter 3.6
 practice exercises, notes
 HW, quizzes, test
22
 3
 manipulate, simplify and graph rational functions, determining end behavior and asymptotes
 12.3.1[a,b,d,e]
12.3.3[b,d,e,j,k,l]
horizontal, vertical and slant asymptote
 textbook, chapter 3.7
 practice exercises, notes
 HW, quizzes, test











write a polynomial function for a given situation and find the maximum or minimum value of the function
 12.2.5.a
 2
 cubic functions, maximum, minimum






1
 location principle





































































































21
 1
 graph functions of two variables in a two-dimensional coordinate system and read such graphs
 12.3.1.a, 12.3.2.ad
 1
 curves of constant values
 textbook, chapter
 practice exercises, notes
 HW, quizzes, test
22
 1
 form functions of one variable from a verbal description and determine the minimum or maximum value of the function
 12.2.4.b, 12.2.5.af, 12.3.2.ad
 1
textbook, chapter
 practice exercises, notes
 HW, quizzes, test









23
 1
 define and apply integral exponents and rational exponents
 12.1.1.b, 12.1.3.b, 12.3.1.a, 12.3.2.d
 2
 growth and decay, laws of exponents
 textbook, chapter 5
 practice exercises, notes
 HW, quizzes, test
24
 1
 define and use exponential functions
 12.3.1.a, 12.3.2.a, 12.3.2.d
 1
 rule of 72, half-life
 textbook, chapter 5
 practice exercises, notes
 HW, quizzes, test
25
 1
 define and apply the natural exponential function
 12.3.1.a, 12.3.2.a, 12.3.2.d
 1
 natural exponential function, compound interest, effective annual yield
 textbook, chapter 5
 practice exercises, notes
 HW, quizzes, test
26
 1
 define and apply logarithms and prove and apply laws of logarithms
 12.1.3
 2
 common logarithm, natural logarithm
 textbook, chapter 5
 practice exercises, notes
 HW, quizzes, test
27
 1
 solve exponential equations and change logarithms from one base to another
 12.1.3.b, 12.3.3
 1
 exponential equation, change-of-base formula
 textbook, chapter 5
 practice exercises, notes
 HW, quizzes, test
28
 1
 find equations of circles, ellipses, hyperbolas and parabolas and graph them
 12.2.1.g, 12.3.1.d, 12.3.1.e
 4
 circle, ellipse, hyperbola, parabola, conic sections, center, radius, focus, foci, directrix, asymptotes
 textbook, chapter 6
 practice exercises, notes
 HW, quizzes, test
29
 1
 solve systems of second-degree equations
 12.3.3
 1
textbook, chapter 6
 practice exercises, notes
 HW, quizzes, test
30
 1
 define conic sections in terms of eccentricity and classify the graph of a second-degree equation by examining the coefficients
 12.3.2.d
 1
 eccentricity, non-degenerate conic sections
 textbook, chapter 6
 practice exercises, notes
 HW, quizzes, test
31
 2
 find the measure of an angle in either degrees or radians and find coterminal angles
 12.2.5
 1
 initial ray, terminal ray, revolution, degree, minutes, seconds, radian, standard position, coterminal
 textbook, chapter 7
 practice exercises, notes
 HW, quizzes, test
32
 2
 find the arc length and area of a sector of a circle and solve problems involving apparent size
 12.2.5, 12.2.5.e, 12.3.2
 1
 arc length, sector, apparent size
 textbook, chapter 7
 practice exercises, notes
 HW, quizzes, test
33
 2
 use the definitions of sine and cosine to find values of these functions and solve simple trigonometric equations
 12.2.1, 12.2.2, 12.3.1
 1
 sine, cosine, unit circle
 textbook, chapter 7
 practice exercises, notes
 HW, quizzes, test
34
 2
 use reference angles, calculators or tables, and special angles to find values of the sine and cosine functions and sketch graphs of these functions
 12.2.1, 12.2.2, 12.3.1
 2
 reference angle, latitude
 textbook, chapter 7
 practice exercises, notes
 HW, quizzes, test
35
 2
 find values of the tangent, cotangent, secant, and cosecant and sketch the functions graphs
 12.2.1, 12.2.2, 12.3.1
 1
 tangent, cotangent, secant, cosecant
 textbook, chapter 7
 practice exercises, notes
 HW, quizzes, test
36
 2
 find values of inverse trigonometric functions
 12.2.1, 12.2.2, 12.3.1, 12.3.1.h
 1
textbook, chapter 7
 practice exercises, notes
 HW, quizzes, test
37
 2
 solve simple trigonometric equations and apply them and find angles of inclination
 12.3.2, 12.3.3
 1
 angle of inclination
 textbook,
chapter 8
 practice exercises, notes
 HW, quizzes, test
38
 2
 find equations of different sine and cosine curves and apply these equations
 12.3.2, 12.3.3
 2
 period, amplitude
 textbook,
chapter 8
 practice exercises, notes
 HW, quizzes, test
39
 2
 use trigonometric functions to model periodic behavior
 12.3.1, 12.3.2, 12.3.3
 2
 axis of the wave
 textbook,
chapter 8
 practice exercises, notes
 HW, quizzes, test
40
 2
 simplify trigonometric expressions and prove trigonometric identities
 12.3.1, 12.3.2, 12.3.3
 1
 reciprocal relationships,
negative relationships,
pythagorean relationships, cofunction relationships
 textbook,
chapter 8
 practice exercises, notes
 HW, quizzes, test
41
 2
 use trigonometric identities or technology to solve more difficult trigonometric equations
 12.3.1, 12.3.2, 12.3.3
 2
textbook,
chapter 8
 practice exercises, notes
 HW, quizzes, test
42
 2
 use trigonmetry to find unkown sides or angles of a right triangle
 12.3.1, 12.3.2, 12.3.3
 1
 angle of elevation, angle of depression
 textbook,
chapter 9
 practice exercises, notes
 HW, quizzes, test
43
 2
 find the area of a triangle given the lengths of two sides and the measure of the included angle
 12.2.5, 12.3.3
 1
 included angle
 textbook,
chapter 9
 practice exercises, notes
 HW, quizzes, test
44
 2
 use the law of sines find unkown parts of a triangle
 12.3.2, 12.3.3
 1
 law of sines
 textbook,
chapter 9
 practice exercises, notes
 HW, quizzes, test
45
 2
 use the law of cosines find unkown parts of a triangle
 12.3.2, 12.3.3
 1
 law of cosines
 textbook,
chapter 9
 practice exercises, notes
 HW, quizzes, test
46
 2
 use trigonometry to solve navigation and surveying problems
 12.2.4, 12.3.1, 12.3.2, 12.3.3
 1
 compass bearing, course
 textbook,
chapter 9
 practice exercises, notes
 HW, quizzes, test
47
 2
 derive and apply sum and difference formulas for sine and cosine
 12.3.1, 12.3.2, 12.3.3
 1
textbook,
chapter 10
 practice exercises, notes
 HW, quizzes, test
48
 2
 derive and apply sum and difference formulas for tangent
 12.3.1, 12.3.2, 12.3.3
 1
textbook,
chapter 10
 practice exercises, notes
 HW, quizzes, test
49
 2
 derive and apply double and half angle formulas for sine, cosine, and tangent
 12.3.1, 12.3.2, 12.3.3
 2
textbook,
chapter 10
 practice exercises, notes
 HW, quizzes, test
50
 2
 use identities to solve trigonometric equations
 12.3.1, 12.3.2, 12.3.3
 2
textbook,
chapter 10
 practice exercises, notes
 HW, quizzes, test
51
 2
 convert polar to rectangular and rectangular to polar coordinates and graph polar equations
 12.2.2, 12.3.1, 12.3.2, 12.3.3
 1
 polar coordinates, polar equation, polar graph
 textbook,
chapter 11
 practice exercises, notes
 HW, quizzes, test
52
 2
 write complex numbers in polar form and find products in polar form
 12.2.2, 12.3.1, 12.3.2, 12.3.3
 1
 argand diagram, complex number plane, polar angle
 textbook,
chapter 11
 practice exercises, notes
 HW, quizzes, test
53
 2
 use DeMoivre's theorem to find powers of complex numbers
 12.2.2, 12.3.1, 12.3.2, 12.3.3
 1
 DeMoivre's theorem
 textbook,
chapter 11
 practice exercises, notes
 HW, quizzes, test
54
 2
 find roots of complex numbers
 12.2.2, 12.3.1, 12.3.2, 12.3.3
 1
textbook,
chapter 11
 practice exercises, notes
 HW, quizzes, test
55
 3
 identify an arithmetic or geometric sequence and find a formula for its nth term
 12.3.1, 12.3.2, 12.3.3
 1
 arithmetic sequence,
geometric sequence
 textbook,
chapter 13
 practice exercises, notes
 HW, quizzes, test
56
 3
 use sequences defined recursively to solve problems
 12.3.1, 12.3.2, 12.3.3
 1
 recursive definition
 textbook,
chapter 13
 practice exercises, notes
 HW, quizzes, test
57
 3
 find the sum of the first n terms of arithmetic or geometric series
 12.3.1, 12.3.2, 12.3.3
 1
 finite sequences, finite series, infinite sequences, infinite series
 textbook,
chapter 13
 practice exercises, notes
 HW, quizzes, test
58
 3
 find or estimate the limit of an ifinite sequence or determine that the limit does not exist
 12.3.1, 12.3.2, 12.3.3
 1
 infinite limits
 textbook,
chapter 13
 practice exercises, notes
 HW, quizzes, test
60
 3
 find the sum of an infinite geometric series
 12.3.1, 12.3.2, 12.3.3
 1
 converge, diverge
 textbook,
chapter 13
 practice exercises, notes
 HW, quizzes, test
61
 3
 represent series using sigma notation
 12.3.1, 12.3.2, 12.3.3
 1
 sigma notation, summand, limits of summation, index
 textbook,
chapter 13
 practice exercises, notes
 HW, quizzes, test
62
 4
 find the limit of a function or the quotient of two functions and to determine whether a function is continuous
 12.3.1, 12.3.2, 12.3.3
 1
 continuous
 textbook,
chapter 19
 practice exercises, notes
 HW, quizzes, test